Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to Random Walks in Random Media

Cecile Monthus

Published 2021-01-22Version 1

The inference of Markov models from data on stochastic dynamical trajectories over the time-window $T$ is revisited via the large deviations at Level 2.5 for the time-empirical density and the time-empirical flows in order to obtain the large deviations properties of the inferred Markov parameters for large $T$. The explicit rate functions are given for several settings, namely discrete-time Markov chains, continuous-time Markov jump processes, and diffusion processes in dimension $d$. Applications to various models of random walks in random media are described, where the goal is to infer the quenched random variables defining a given disordered sample.